Front spoilers reduce lift by coaching the air around the car instead of under it. The absence of lift could be considered downforce but it's not really. Think of it as being a car with 2000 lbs nose weight but at 70MPH the lift it experiences effectively makes the nose weigh 1800 lbs. A spoiler reduces or eliminates that lift. Downforce means that there is now say 2200 lbs on the nose as the car moves through the air. Splitters and such are typically downforce generators, as would be the example of a car where the radiator is ducted so that air escapes through the hood against a panel. Look at the Euro Touring car series for an idea of how they manipulate air for downforce, especially the DTM (German Touring Cars).
A rear spoiler like on the 1st-gen Camaros & etc actually causes the air coming over the roof to hit the trunk lid, as well as breaking up the eddy that forms behind the car. The trade-off with rear aero devices, as well as big cooling openings & add-ons like mirrors & etc is drag.
To an extent, you can think of a car moving through air as a stationary object in moving water, although it's a bit more complicated than that, which is why the better wind tunnels now use moving floors.